Last week was the beginning of a program at the Santa Barbara KITP entitled The Harmony of Scattering Amplitudes which will focus on topics including recent advances in computing N=4 super Yang-Mills scattering amplitudes. Talks are available on-line here. There’s a full schedule of talks in the program and related talks here. On Thursday, Nima Arkani-Hamed will give a talk on “The planar integrand of N=4 super-Yang-Mills theory”, which some wag has scheduled as lasting from 1:30pm to 5am.
For a survey of some of these recent developments, a correspondent points me to the thesis of Arkani-Hamed’s student Jacob Bourjaily, which has just appeared online here.
Interesting that the Spradlin talk mentions motives and Hopf algebras in passing, since he has been working with the mathematician Goncharov (et al) to obtain a short expression for the 2 loop 6 pt amplitude in N=4 SYM. There was a bit too much talk about being in a ‘cult’ though.
The linked article says in the first paragraph “With the imminent arrival of the Large Hadron Collider (LHC) at CERN, it is clear that in the coming years scattering amplitudes and cross-sections will take on an even more prominent role in particle physics.”
I have a hard time believing their work on N=4 SYM and N=8 SUGRA would shed much light on QCD processes at LHC. Can someone explain to me to what extend will this be true?
Oops, there’s no such thing as “imminent arrival”. The LHC has arrived for some time.
Anon, as explained in the first (technical) talk, the original Parke Taylor MHV (tree) amplitude is just as valid for QCD as for N=4 SYM. For this reason alone N=4 SYM is worth pursuing, and one might also note that SUSY aspects are rather easy to separate out from the other degrees of freedom. That is, there is every reason to believe that real QCD has a similar non local formulation in terms of motivic Galois theory (whatever that is).
Remember that even the original Parke-Taylor QCD calculation was done by using susy arguments.
I’m also skeptical about the application of all this stuff to theories with less SUSY. For example, a simple argument shows that (+++…+) and (-++…+) amplitudes vanish to all orders in N=4 SYM, but this is not true for theories with less supersymmetry. I saw Nima give a talk recently, and this was one of many crucial points which seemed to rely heavily on having N=4.
XENON 100 announces the result!
There are several ways in which information from amplitudes in supersymmetric theories can be used in practical QCD calculations up to one-loop. Let me mention three
– At tree level susy and non-susy theories are not that different: fermion lines do not show up in the diagrams of purely bosonic amplitudes. There is a story for what happens to tree amplitudes with quarks (bottomline: you can extract the QCD quark amplitudes from the N=4 ones).
– Tree amplitudes appear in unitarity cuts of one loop amplitudes, also in QCD. There are known ways to use this information to calculate the full loop amplitudes. This includes the amplitudes with helicity +++…+ configuration for instance.
– last but not least: people write actual numerical code for calculating QCD amplitudes using methods inspired by all the N=4 type stuff (BLACKHAT, ROCKET, etc, etc).